Hooke's Law should be exponential.

[JCienfuegos]

I was just thinking, shouldn't hooke's law be represented with an exponential equation?
I am thinking that in class, the springs we use for the hooke's law experiment are small, but if they were very large, then the higher coils would be sustaining much more weight than the lower coils, and would thus be stretched more. I think this would lend itself more to an exponential model.

 

[NascentOxygen]

I guess the ideal model spring represented in Mr Hooke's law is one that is perfectly elastic and quite weightless.

Feel free to come up with a more accurate model for the ones in your lab. But be warned, you'll then have to look for some other plausible reason for your measurements not tallying so well with theory. Inaccurate modelling is always such a convenient excuse for general disagreement between theory and practice!

 

[Khashishi]

If you are familiar with Taylor series expansions, then you can understand that any system with a non-vanishing linear term in the expansion will behave close to linear for a perturbation from the equilibrium point sufficiently small. So, Hooke's law is trivial, but it works pretty well in practice.

 

[nasu]

I was just thinking, shouldn't hooke's law be represented with an exponential equation?
I am thinking that in class, the springs we use for the hooke's law experiment are small, but if they were very large, then the higher coils would be sustaining much more weight than the lower coils, and would thus be stretched more. I think this would lend itself more to an exponential model.

Hooke's law states that the strain (deformation) is proportional to the stress (tension, force). How will this be modified by the weight of the spring?
The deformation won't be uniform (as it is for weightless or horizontal spring on a table) but Hooke's law still applies as it is. In each piece of spring, the deformation will be proportional to the tension in that region. However the tension varies along the spring.
You can apply Hooke's law to find the deformation of an elastic bar or cable under its own weight.

Only if the deformation is too large Hooke's law will fail but this is not really related to the size of the spring or the existence of gravity. If you take a very small spring and you pull it hard enough, it won't get back to original size and shape. This is an example of non-elastic behavior.